\[ -a+y(x) y''(x)+y'(x)^2=0 \] ✓ Mathematica : cpu = 0.182406 (sec), leaf count = 94
\[\left \{\left \{y(x)\to -\frac {\sqrt {a^2 x^2+2 a^2 c_2 x+a^2 c_2{}^2-e^{2 c_1}}}{\sqrt {a}}\right \},\left \{y(x)\to \frac {\sqrt {a^2 x^2+2 a^2 c_2 x+a^2 c_2{}^2-e^{2 c_1}}}{\sqrt {a}}\right \}\right \}\] ✓ Maple : cpu = 0.894 (sec), leaf count = 39
\[y \relax (x ) = \sqrt {a \,x^{2}-2 c_{1} x +2 c_{2}}\]